The flow structure predicted in the vicinity of free-stream edges by two-equation eddy-viscosity turbulence models is examined. Analytical expansions, previously used by several authors, are shown to be weak solutions to the pure nonlinear diffusion problem, connecting with trivial solutions in the nonturbulent region. They remain locally valid solutions to the full one-dimensional system of model equations in the vicinity of the edge, provided that some constraints on the turbulent "Prandtl numbers" are satisfied. Calculations performed with the (k,€) turbulence model for a time-evolving mixing layer and a flat-plate boundary layer in zero pressure gradient are fully consistent with the analysis. In contradiction of a prior study by Lele [Phys. Fluids 28, 64 (1985)], the modeled turbulent-kinetic-energy, dissipation-rate, and shear-stress fronts are found to propagate into the nonturbulent region at the same velocity, with no need for any special relationship between the model constants. Implications related to the calibration of models are discussed.
The possibility to take into account the effects of the Coriolis acceleration on turbulence is examined in the framework of two-equation eddy-viscosity models. General results on the physical consistency of such turbulence models are derived from a dynamical-system approach to situations of time-evolving homogeneous turbulence in a rotating frame. Application of this analysis to a ͑k , ⑀͒ model fitted with an existing Coriolis correction ͓J. H. G. Howard, S. V. Patankar, and R. M. Bordynuik, "Flow prediction in rotating ducts using Coriolis-modified turbulence models," ASME Trans. J. Fluids Eng. 102, 456 ͑1980͔͒ is performed. Full analytical solutions are given for the flow predicted with this model in the situation of homogeneously sheared turbulence subject to rotation. The existence of an unphysical phenomenon of blowup at finite time is demonstrated in some range of the rotation-to-shear ratio. A direct connection is made between the slope of the mean-velocity profile in the plane-channel flow with spanwise rotation, and a particular fixed point of the dynamical system in homogeneously sheared turbulence subject to rotation. The general analysis, and the understanding of typical inaccuracies and misbehavior observed with the existing model, are then used to design a new model which is free from the phenomenon of blowup at finite time and able to account for both of the main influences of rotation on turbulence: the inhibition of the spectral transfer to high wave numbers and the shear/Coriolis instability.
This article focuses on the practical use of the similarity principle for centrifugal compressor design, i.e. geometrical scaling of existing impellers to meet new specifications. Basic principles of similarity are first used to derive scaling laws. Then, the analysis of typical specifications and the use of partial similarity (neglecting the Reynolds-number effects) allows the use of the pressure ratio-specific speed diagram so that a compressor can be scaled along its best-efficiency operating line. A practical method is proposed to use these scaling laws in a design context, in order to define the scaling potential of an existing stage as the ensemble of specifications that can be met by scaling. Finally, the scaling potential of an industrial compressor is evaluated and represented as a surface in the 3D space defined by the similarity variables, with the associated efficiency variations.
The modeling of the turbulent diffusion of quantities such as the turbulent kinetic energy and its dissipation rate in the outer part of wall-bounded flows is examined with the aid of simulation data. The channel-flow data of Mansour et al. [J. Fluid Mech. 194, 15 (1988)] and those of Spalart [J. Fluid Mech. 187, 61 (1988)] for a flat-plate boundary layer with zero pressure gradient are used to examine the differences between turbulent flows with and without a free-stream edge. The ratio of the diffusivity of the above-mentioned turbulent quantities to the diffusivity of momentum is roughly constant, as assumed in most models, and little affected by the presence of the free-stream edge. However, the diffusivity ratios are found to deviate significantly from so-called ‘‘standard’’ values. Furthermore, current models for the momentum diffusivity fail badly at the edge of the boundary layer: the modeling constant Cμ used in the (k,ε) and related models exhibits a rapid rise there. In this respect, the simulation data confirm earlier experimental studies. The consequences of these findings for turbulence modeling are briefly examined.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.